Question

The value of a new car depreciates (decreases) after it is purchased. Suppose that the value of the car depreciates according to an exponential decay model. Suppose that the value of the car is $12000 at the end of 5 years and that its value has been decreasing at the rate of 9% per year. Find the value of the car when it was new.

Answer 1

The value of the car when it was new can be found using the exponential decay formula. Given that the car's value is $12,000 after 5 years with a depreciation rate of 9% per year, the value when it was new is approximately $18,006.67.

Step-by-step explanation:

To find the value of the car when it was new, we can use the formula for exponential decay:

Value = Initial Value * e^(rate * time)

Let x be the value of the car when it was new. We are given that after 5 years, the value is $12,000 and the rate of depreciation is 9% per year. Plugging these values into the formula:

12000 = x * e^(-0.09 * 5)

Solving for x gives us:

x = 12000 / e^(-0.09 * 5)

Calculating this value gives us:

x ≈ $18,006.67

Therefore, the value of the car when it was new is approximately $18,006.67.